# Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

### Submission summary

 As Contributors: Grégoire Misguich Arxiv Link: https://arxiv.org/abs/2011.08052v1 (pdf) Date submitted: 2020-11-17 11:00 Submitted by: Misguich, Grégoire Submitted to: SciPost Physics Academic field: Physics Specialties: Mathematical Physics Statistical and Soft Matter Physics Approach: Theoretical

### Abstract

We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group $U_q(\widehat{sl}_n)$. Compared with the conventional $(n-1)$-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also introduce a randomized cBBS and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.

###### Current status:
Editor-in-charge assigned